Remark 3.13 Using results from [1]}, in the special case \((p,n)=1\) , we can extend Corollary REF  to much larger generality. Indeed, if \(f:Y \rightarrow X\)  is any separated taut morphism of rigid spaces over \(K\) , then \(Rf^!\)  sends \(D^{(b)}_{zc}(X,\mathbf {Z}/n)\)  into \(D^{(b)}_{zc}(Y,\mathbf {Z}/n)\) . To see this, by Theorem REF , this assertion can be checked locally on \(X\)  and \(Y\) , so we can assume they are affinoid. The map \(f\)  can be then be factored as the composition of a Zariski-closed immersion followed by a smooth map of pure dimension \(d\) . The claim for Zariski-closed immersions follows from Corollary REF , while that for smooth morphisms follows from Huber's [1]}, which identifies \(Rf^!\)  with \(f^*(d)[2d]\) .

